Answer
$x = -1$ or $x = \dfrac{1}{3}$
Work Step by Step
The quadratic formula is given as $x = \dfrac{-b ± \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the first term, $b$ is the coefficient of the second term, and $c$ is the constant term.
The given quadratic equation has $a=3, b=2, \text{ and } c=-1$. Substitute these values into the quadratic formula:
$x = \dfrac{-2 ± \sqrt {2^2 - 4(3)(-1)}}{2(3)}$
$x = \dfrac{-2 ± \sqrt {4 - 4(3)(-1)}}{2(3)}$
$x = \dfrac{-2 ± \sqrt {4 + 12}}{6}$
$x = \dfrac{-2 ± \sqrt {16}}{6}$
Take the square root:
$x = \dfrac{-2 ± 4}{6}$
$x = \dfrac{-2-4}{6}\quad$ or $\quad x = \dfrac{-2+4}{6}$
$x = \dfrac{-6}{6}\quad$ or $\quad x = \dfrac{2}{6}$
$x = -1\quad $ or $\quad x = \dfrac{1}{3}$
